Axioms For Lattices And Boolean Algebras
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Axioms For Lattices And Boolean Algebras
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Author : Ranganathan Padmanabhan
language : en
Publisher: World Scientific
Release Date : 2008
Axioms For Lattices And Boolean Algebras written by Ranganathan Padmanabhan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The importance of equational axioms emerged initially with the axiomatic approach to Boolean algebras, groups, and rings, and later in lattices. This unique research monograph systematically presents minimal equational axiom-systems for various lattice-related algebras, regardless of whether they are given in terms of ?join and meet? or other types of operations such as ternary operations. Each of the axiom-systems is coded in a handy way so that it is easy to follow the natural connection among the various axioms and to understand how to combine them to form new axiom systems. A new topic in this book is the characterization of Boolean algebras within the class of all uniquely complemented lattices. Here, the celebrated problem of E V Huntington is addressed, which ? according to G Gratzer, a leading expert in modern lattice theory ? is one of the two problems that shaped a century of research in lattice theory. Among other things, it is shown that there are infinitely many non-modular lattice identities that force a uniquely complemented lattice to be Boolean, thus providing several new axiom systems for Boolean algebras within the class of all uniquely complemented lattices. Finally, a few related lines of research are sketched, in the form of appendices, including one by Dr Willian McCune of the University of New Mexico, on applications of modern theorem-proving to the equational theory of lattices.
Ordered Sets And Lattices Ii
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date :
Ordered Sets And Lattices Ii written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativnyi Zhurnal Matematika from mid-1982 to the end of 1985. A continuation of a previous volume (the English translation of which was published by the AMS in 1989, as volume 141 in Translations - Series 2), this comprehensive work contains more than 2200 references. Many of the papers covered here were originally published in virtually inaccessible places. The compilation of the volume was directed by Milan Kolibiar of Comenius University at Bratislava and Lev A. Skornyakov of Moscow University. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.
Modern Algebra
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Author : John R. Durbin
language : en
Publisher: John Wiley & Sons
Release Date : 2008-12-31
Modern Algebra written by John R. Durbin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-31 with Mathematics categories.
The new sixth edition of Modern Algebra has two main goals: to introduce the most important kinds of algebraic structures, and to help students improve their ability to understand and work with abstract ideas. The first six chapters present the core of the subject; the remainder are designed to be as flexible as possible. The text covers groups before rings, which is a matter of personal preference for instructors. Modern Algebra, 6e is appropriate for any one-semester junior/senior level course in Modern Algebra, Abstract Algebra, Algebraic Structures, or Groups, Rings and Fields. The course is mostly comprised of mathematics majors, but engineering and computer science majors may also take it as well.
Qualitative Spatio Temporal Representation And Reasoning Trends And Future Directions
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Author : Hazarika, Shyamanta M.
language : en
Publisher: IGI Global
Release Date : 2012-05-31
Qualitative Spatio Temporal Representation And Reasoning Trends And Future Directions written by Hazarika, Shyamanta M. and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-31 with Computers categories.
Space and time are inextricably linked. Reasoning about space often involves reasoning about change in spatial configurations. Qualitative spatial information theory encompasses spatial as well as temporal representation and reasoning. Qualitative Spatio-Temporal Representation and Reasoning: Trends and Future Directions is a contribution to the emerging discipline of qualitative spatial information theory within artificial intelligence. This collection of research covers both theory and application-centric research and provides a comprehensive perspective on the emerging area of qualitative spatio-temporal representation and reasoning. This revolutionary new field is increasingly becoming a core issue within mobile computing, GIS/spatial information systems, databases, computer vision as well as knowledge discovery and data mining.
Introduction To Discrete Mathematics Via Logic And Proof
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Author : Calvin Jongsma
language : en
Publisher: Springer Nature
Release Date : 2019-11-08
Introduction To Discrete Mathematics Via Logic And Proof written by Calvin Jongsma and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-08 with Mathematics categories.
This textbook introduces discrete mathematics by emphasizing the importance of reading and writing proofs. Because it begins by carefully establishing a familiarity with mathematical logic and proof, this approach suits not only a discrete mathematics course, but can also function as a transition to proof. Its unique, deductive perspective on mathematical logic provides students with the tools to more deeply understand mathematical methodology—an approach that the author has successfully classroom tested for decades. Chapters are helpfully organized so that, as they escalate in complexity, their underlying connections are easily identifiable. Mathematical logic and proofs are first introduced before moving onto more complex topics in discrete mathematics. Some of these topics include: Mathematical and structural induction Set theory Combinatorics Functions, relations, and ordered sets Boolean algebra and Boolean functions Graph theory Introduction to Discrete Mathematics via Logic and Proof will suit intermediate undergraduates majoring in mathematics, computer science, engineering, and related subjects with no formal prerequisites beyond a background in secondary mathematics.
Handbook Of Mathematical Induction
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Author : David S. Gunderson
language : en
Publisher: CRC Press
Release Date : 2014-01-09
Handbook Of Mathematical Induction written by David S. Gunderson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Computers categories.
Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics.In the first part of the book, the author discuss
Modern Algebra With Applications
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Author : William J. Gilbert
language : en
Publisher: John Wiley & Sons
Release Date : 2004-01-30
Modern Algebra With Applications written by William J. Gilbert and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-30 with Mathematics categories.
Praise for the first edition "This book is clearly written and presents a large number ofexamples illustrating the theory . . . there is no other book ofcomparable content available. Because of its detailed coverage ofapplications generally neglected in the literature, it is adesirable if not essential addition to undergraduate mathematicsand computer science libraries." –CHOICE As a cornerstone of mathematical science, the importance ofmodern algebra and discrete structures to many areas of science andtechnology is apparent and growing–with extensive use incomputing science, physics, chemistry, and data communications aswell as in areas of mathematics such as combinatorics. Blending the theoretical with the practical in the instructionof modern algebra, Modern Algebra with Applications, Second Editionprovides interesting and important applications of thissubject–effectively holding your interest and creating a moreseamless method of instruction. Incorporating the applications of modern algebra throughout itsauthoritative treatment of the subject, this book covers the fullcomplement of group, ring, and field theory typically contained ina standard modern algebra course. Numerous examples are included ineach chapter, and answers to odd-numbered exercises are appended inthe back of the text. Chapter topics include: Boolean Algebras Polynomial and Euclidean Rings Groups Quotient Rings Quotient Groups Field Extensions Symmetry Groups in Three Dimensions Latin Squares Pólya—Burnside Method of Enumeration Geometrical Constructions Monoids and Machines Error-Correcting Codes Rings and Fields In addition to improvements in exposition, this fully updatedSecond Edition also contains new material on order of an elementand cyclic groups, more details about the lattice of divisors of aninteger, and new historical notes. Filled with in-depth insights and over 600 exercises of varyingdifficulty, Modern Algebra with Applications, Second Edition canhelp anyone appreciate and understand this subject.
Numbers Sets And Axioms
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Author : A. G. Hamilton
language : en
Publisher: Cambridge University Press
Release Date : 1982
Numbers Sets And Axioms written by A. G. Hamilton and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.
Algebraic Methods In General Rough Sets
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Author : A. Mani
language : en
Publisher: Springer
Release Date : 2019-01-11
Algebraic Methods In General Rough Sets written by A. Mani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-11 with Mathematics categories.
This unique collection of research papers offers a comprehensive and up-to-date guide to algebraic approaches to rough sets and reasoning with vagueness. It bridges important gaps, outlines intriguing future research directions, and connects algebraic approaches to rough sets with those for other forms of approximate reasoning. In addition, the book reworks algebraic approaches to axiomatic granularity. Given its scope, the book offers a valuable resource for researchers and teachers in the areas of rough sets and algebras of rough sets, algebraic logic, non classical logic, fuzzy sets, possibility theory, formal concept analysis, computational learning theory, category theory, and other formal approaches to vagueness and approximate reasoning. Consultants in AI and allied fields will also find the book to be of great practical value.
The Art Of The Intelligible
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Author : J. Bell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Art Of The Intelligible written by J. Bell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
A compact survey, at the elementary level, of some of the most important concepts of mathematics. Attention is paid to their technical features, historical development and broader philosophical significance. Each of the various branches of mathematics is discussed separately, but their interdependence is emphasised throughout. Certain topics - such as Greek mathematics, abstract algebra, set theory, geometry and the philosophy of mathematics - are discussed in detail. Appendices outline from scratch the proofs of two of the most celebrated limitative results of mathematics: the insolubility of the problem of doubling the cube and trisecting an arbitrary angle, and the Gödel incompleteness theorems. Additional appendices contain brief accounts of smooth infinitesimal analysis - a new approach to the use of infinitesimals in the calculus - and of the philosophical thought of the great 20th century mathematician Hermann Weyl. Readership: Students and teachers of mathematics, science and philosophy. The greater part of the book can be read and enjoyed by anyone possessing a good high school mathematics background.